Problem: Solve for $x$ and $y$ using elimination. ${2x+6y = 10}$ ${-2x+5y = 1}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $11y = 11$ $\dfrac{11y}{{11}} = \dfrac{11}{{11}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {2x+6y = 10}\thinspace$ to find $x$ ${2x + 6}{(1)}{= 10}$ $2x+6 = 10$ $2x+6{-6} = 10{-6}$ $2x = 4$ $\dfrac{2x}{{2}} = \dfrac{4}{{2}}$ ${x = 2}$ You can also plug ${y = 1}$ into $\thinspace {-2x+5y = 1}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(1)}{= 1}$ ${x = 2}$